The Necker cube is a classic example of a reversible figure in visual perception. It appears as a simple wireframe cube, but the mind alternates between two interpretations of its orientation:
- Either the front face projects outward, or the back face does.
- Both orientations are equally valid, but they cannot be perceived simultaneously.
Necker Cube and Chiralkine Counting
The alternating perceptions of the Necker cube offer a powerful analogy for chiralkine counting, where relationships are defined symmetrically as mirror opposites:
- Dual Interpretations:
In the Necker cube, the two orientations correspond to the dual relationships inherent in chiralkine counting—“is” and “not.”- Each perception defines the cube from a distinct point of view, much like how chiralkine counting defines objects through symmetrical oppositions.
- Symmetry and Cycling:
As the mind flips between the two orientations, it mirrors the cyclical rotation in chiralkine counting, where distinctions between relationships evolve in a structured, repeating pattern. - Ambiguity and Completeness:
The Necker cube’s ambiguity highlights a key principle in chiralkine counting:- Both perspectives are equally valid, but only when considered together do they represent the cube’s full structure.
- Similarly, chiralkine counting accounts for both sides of a relationship, treating them symmetrically to avoid privileging one over the other.
Visualizing Relationships
To connect the Necker cube more directly to chiralkine counting, consider marking its faces or edges with additive and subtractive colors.
These colors would:
- Represent the dual relationships defining each face.
- Make the symmetrical nature of the cube’s alternating orientations explicit.
Conclusion
The Necker cube illustrates how perception toggles between dual, valid interpretations. This aligns beautifully with the principles of chiralkine counting, where symmetry, duality, and cyclical relationships define the system. By exploring this analogy, we gain deeper insight into how chiralkine counting frames relationships and systems without privileging one perspective over another.
Footnote
The cube can be modelled as two interpenetrating mirror opposite tetrahedrons each having four corners a, b, c, d. The arrangement is such that the corners of the hexagon are ordered a, b, c, a, b, c.
The Necker cube effect models chiralkine counting better than a cube, because what appears to be the central “point” is always two points, one up and one down. In a cube the diagonals connecting the corners cross at one imaginary point, at which imaginary point opposed corners are one and the same. The features of the Necker cube are present independent of scale. The opposed corners and their behaviour as the Necker cube is “rotated” in space from one face to another are conserved no matter how small the Necker cube is shrunk.
The d in the diagram above, which represents the illusion of projection above or below the plane, is nothing other than the counterpart to one of the other three objects. This can best be appreciated by reviewing the page on how chiralkine counting works with particular reference to the drawing reproduced below.
The d’s in the centre of the Necker cube are the next of a, b and c to come into view to complete the fourth corner of a face. The system behaves like a fractal.
